If y(t) is the solution of - 2y = 4, y(0) =1, then y(t)= %3D %3D

Q: Solve the initial-value problem using the method of undetermined coefficients. y" + 5y' – 6y = 8e2x;…

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Q: Solve the initial value problem using the method of undetermined coefficients.  y"+4y'+4y=(3+x)e-2x,…

A: The given intial value problem is given by,

Q: Let y (t) be the solution of the initial value problem y" – 4y' + 5y = e-2t %3D 1 and y' (0) = 17 y…

A: We have to observe the characteristic equation first.

Q: Given the initial condition y(0) = 1, find the particular solution of the equation yy' - 6x = 0

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Q: Find the particular solution for initial value problem.

A: dydx=8x3-3x2+7x having initial value y3=0

Q: (b) Use the method of complementary functions and particular solutions, to determine the general…

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Q: The general solution of y" - 2y' +y= e* cos(x) is

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Q: y′−6x=5+2y y(0)=−3 Is y=e2x −3x−4 a solution to the initial value problem shown above?

A: The given differential equation is y′−6x=5+2y.The solution of the deferential equation is given as,…

Q: 4xyy’ = y^2+x^2 y(1)=1  find the specific solution of the initial value problem

A: We will solve the problem.

Q: Directly using the Laplace transform

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Q: True or False The initial value problem  dx/dt = ax3 + 2x^2 x(0) = b has a unique solution for any…

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Q: find the solution satisfying the initial conditions: y''-y=x^2 , y(0)=0 , y'(0)=-1

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Q: The solution of the initial value problem dy - -2xy, y(0) = 2 is %3D

A: We can solve this question as below

Q: Find the general solution of y" – 3y' + 2y 1+e-x°

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Q: 1. Find the general solution of dy dx + y = x

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Q: solve the initial value problem. dy/dx + 3x2y = x2, y(0) = -1

A: Given differential equation is dydx+3x2y=x2 Comparing it with the general linear differential…

Q: Find the solution of the initial-value problem dy - 2y = 2.x", y(2) = 8. dx

A: Convert this IVP into linear differential equation by dividing by x then proceed to fund Integrating…

Q: xy²dx + e*dy = 0

A: Given differential equation is xy2dx+exdy=0

Q: (b) Solve the initial value problem with seperation of variables and give your solution in the form…

A: Solve differential by using variable separable method

Q: * = y +z- 4x Solve: dt = x+ 5y - z # = y - 3z

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Q: Find the general solution of dy xy = 1+ y?

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Q: (2y +4x)dx- xydy=0 y(1)= -2

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Q: Find the general solution of (3xy-y²)dx-(x²-xy)dy=0

A: As the equation is homogeneous , put y=vx and solve .

Q: How do I find the general solution of y''- 2y'= e^x * sinx using the method of variation of…

A: y''-2y'=ex sin x Auxiliary Equation: m2-2m=0⇒m1=0, m2=2 Complementary function  :  y=c1+c2e2xthis…

Q: For the initial value problem %3D y2 V1+x y(0) = 1, then y(2) = %3D %3D

A: The initial value problem is given as y' = xy21+xdydx = xy21+xy2 dy = x1+xdxy2 dy = x+1-11+xdxy2 dy…

Q: Solve the initial value problem (x + Vy? – xy) = y, G) = 1.

A: Consider the given differential equation. x+y2-xydydx=y Provided that  y12=1 Now, simplifying the…

Q: dy dx Vx² – 16 х d explicit particular solution of the initial value problem 2y- У(5) %3D2

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Q: 3. Find the particular solution of the linear equation dy + -y = dr 1. if y(1) = 0.

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Q: Use variation of parameters to solve the initial value problem, given the solutions y1, y2 of the…

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Q: The solution of y" + y = 0 with initial conditions y (0) = 1 and %3D y = 2 is

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Q: Solve the initial value problem below. x²y" – - 3ry' + 4y = 0, y(1) = F 3, y'(1) = – 1 y =

A: Homogeneous Linear differential equation :   An equation of the form…

Q: Is y=e3x−2x−3 a solution to the initial value problem shown below? y′−3y=6x+7 y(0)=−2   Yes or no?

A: Yes

Q: the solution to the IVP(x2+y2)dy/dx+xy=0 with y(0)=2 is

A: Given DE is x2+y2dydx+xy=0  and y(0)=2 find the solution of the DE

Q: Solve the initial-value problem using the undetermined coefficients at the condition, y(0) = 2,…

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Q: Find an explicit solution of the given initial-value problem. V1- y? dx - V1- x2 dy = 0, y(0) = . y…

A: Solve the following

Q: Find the solution of the initial value problem subject to the indicated initial condition in terms…

A: solution :-

Q: Show that y = x (1 – e*-1) is a solution | to y" – y' + e"-1 = -1

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Q: 4. (a) dzy Solve: dx2 + ( = 0. (b) Solve xy" + (1 – x)y' – 2(1+x)y = e-*(1 – 6x) by the method based…

A: We have, d2ydx2+dydx+dydx3=0 ..i Put dydx=v ⇒d2ydx2=dvdx Now substitute in equation i we get…

Q: Solve the initial value problem using y"+3y'+ 2y = 2u(t-2).y(0) = 0, y (0) = 0

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Q: e general solution to the DE  is(6x+y2)dx+y(2x-3y)dy

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Q: d®y dæ 3 y (0) y' (0) 1 y" (0) = 0 ||

A: Let us consider the differential equation L[D]y=Q(x) Particular solution for the differential…

Q: If f(x, y) = -x - y* + 3xy - 2x - 5y, then in the process of obtaining its critical points the…

A: Introduction: The critical points of the two variables' function f(x,y) is given by solving the two…

Q: 6. Find the general solution of 2x(3x + y – ye-**)dx + (x² + 3y2 + e-**)dy = 0

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Q: Solve the initial value problem. dy +2y-4e¯X = 0, dx The solution is y(x) = y(0) = 2

A: Given differential equation is in the form of linear differential equation . So we will use…

Q: is e^(-3y) is the integrating factor of the FOLDE y'-3y=6, show your solution.

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Q: Solve the initial value problem: d²y 2e-*, y(0) = 1 and y' (0) = 0 dx2

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Q: Solve the initial value problem dy/dx=(x+y+1)2-(x+y-1)2  where y(0)=1/2

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